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Local solutions in Sobolev spaces and unconditional wellposedness for the generalized Boussinesq equation
Crossconstrained variational methods for the nonlinear KleinGordon equations with an inverse square potential
1.  College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068 
[1] 
Hyeongjin Lee, Ihyeok Seo, Jihyeon Seok. Local smoothing and Strichartz estimates for the KleinGordon equation with the inversesquare potential. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 597608. doi: 10.3934/dcds.2020024 
[2] 
Stefano Pasquali. A Nekhoroshev type theorem for the nonlinear KleinGordon equation with potential. Discrete and Continuous Dynamical Systems  B, 2018, 23 (9) : 35733594. doi: 10.3934/dcdsb.2017215 
[3] 
Soichiro Katayama. Global existence for systems of nonlinear wave and kleingordon equations with compactly supported initial data. Communications on Pure and Applied Analysis, 2018, 17 (4) : 14791497. doi: 10.3934/cpaa.2018071 
[4] 
Zheng Han, Daoyuan Fang. Almost global existence for the KleinGordon equation with the Kirchhofftype nonlinearity. Communications on Pure and Applied Analysis, 2021, 20 (2) : 737754. doi: 10.3934/cpaa.2020287 
[5] 
Milena Dimova, Natalia Kolkovska, Nikolai Kutev. Global behavior of the solutions to nonlinear KleinGordon equation with critical initial energy. Electronic Research Archive, 2020, 28 (2) : 671689. doi: 10.3934/era.2020035 
[6] 
ChiKun Lin, KungChien Wu. On the fluid dynamical approximation to the nonlinear KleinGordon equation. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 22332251. doi: 10.3934/dcds.2012.32.2233 
[7] 
Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Kleingordon equation. Discrete and Continuous Dynamical Systems  S, 2021, 14 (5) : 16491672. doi: 10.3934/dcdss.2020448 
[8] 
Guangyu Xu, Chunlai Mu, Dan Li. Global existence and nonexistence analyses to a nonlinear KleinGordon system with damping terms under positive initial energy. Communications on Pure and Applied Analysis, 2020, 19 (5) : 24912512. doi: 10.3934/cpaa.2020109 
[9] 
Katharina Schratz, Xiaofei Zhao. On comparison of asymptotic expansion techniques for nonlinear KleinGordon equation in the nonrelativistic limit regime. Discrete and Continuous Dynamical Systems  B, 2020, 25 (8) : 28412865. doi: 10.3934/dcdsb.2020043 
[10] 
Masahito Ohta, Grozdena Todorova. Strong instability of standing waves for nonlinear KleinGordon equations. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 315322. doi: 10.3934/dcds.2005.12.315 
[11] 
Michinori Ishiwata, Makoto Nakamura, Hidemitsu Wadade. Remarks on the Cauchy problem of KleinGordon equations with weighted nonlinear terms. Discrete and Continuous Dynamical Systems, 2015, 35 (10) : 48894903. doi: 10.3934/dcds.2015.35.4889 
[12] 
Hironobu Sasaki. Remark on the scattering problem for the KleinGordon equation with power nonlinearity. Conference Publications, 2007, 2007 (Special) : 903911. doi: 10.3934/proc.2007.2007.903 
[13] 
Satoshi Masaki, Junichi Segata. Modified scattering for the KleinGordon equation with the critical nonlinearity in three dimensions. Communications on Pure and Applied Analysis, 2018, 17 (4) : 15951611. doi: 10.3934/cpaa.2018076 
[14] 
Karen Yagdjian. The semilinear KleinGordon equation in de Sitter spacetime. Discrete and Continuous Dynamical Systems  S, 2009, 2 (3) : 679696. doi: 10.3934/dcdss.2009.2.679 
[15] 
Aslihan Demirkaya, Panayotis G. Kevrekidis, Milena Stanislavova, Atanas Stefanov. Spectral stability analysis for standing waves of a perturbed KleinGordon equation. Conference Publications, 2015, 2015 (special) : 359368. doi: 10.3934/proc.2015.0359 
[16] 
Elena Kopylova. On dispersion decay for 3D KleinGordon equation. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 57655780. doi: 10.3934/dcds.2018251 
[17] 
Hironobu Sasaki. Small data scattering for the KleinGordon equation with cubic convolution nonlinearity. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 973981. doi: 10.3934/dcds.2006.15.973 
[18] 
Jun Yang. Vortex structures for KleinGordon equation with GinzburgLandau nonlinearity. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 23592388. doi: 10.3934/dcds.2014.34.2359 
[19] 
Changxing Miao, Jiqiang Zheng. Scattering theory for energysupercritical KleinGordon equation. Discrete and Continuous Dynamical Systems  S, 2016, 9 (6) : 20732094. doi: 10.3934/dcdss.2016085 
[20] 
Jungkwon Kim, Hyeongjin Lee, Ihyeok Seo, Jihyeon Seok. On Morawetz estimates with timedependent weights for the KleinGordon equation. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 62756288. doi: 10.3934/dcds.2020279 
2020 Impact Factor: 1.916
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